Theory and practice
We all know about the gap; let’s do something about it.
Kevin C Craig, PhD -- EDN, January 19, 2012
The theory-practice gap has existed for decades, and
each of us must bridge this gap in all we do. Control is
an essential element in all multidisciplinary systems,
so let’s start there and begin to bridge the gap that exists
between the theory of control and its digital implementation.
The following points provide an overview of control theory
for the practitioner.
First, remember that feedback control is a pervasive, powerful, and enabling technology. At first sight, it looks simple and straightforward, but it is amazingly subtle and intricate in both theory and practice. Also remember that you cannot instantaneously effect changes in a dynamic system, so applying an otherwise-correct control decision at the wrong time could result in catastrophe. Further, nonlinearities, including backlash, coulomb friction, saturation, hysteresis, quantization, deadband, and kinematic nonlinearities, are always present. You can use a linearized model to approximate a nonlinear system near an operating point.
When working with dynamic systems, keep in mind that they must have guaranteed stability. Closed-loop systems become unstable because of an imbalance between the strength of corrective action and the system’s dynamic lags. Stable systems must have adequate stability margins to work after you have built them. Stable systems also have a frequency response. If you apply a sinusoidal input to a stable linear system, then the steady-state output will be a sinusoid of the same frequency. The amplitude ratio and phase difference of the two sinusoids are frequency-dependent, however.
Keep in mind that the open-loop transfer function is the
product of all the transfer functions in the loop, including
the controller, the actuator, the plant, and the sensor. The
open-loop transfer function is much less complex than the closed-loop system-transfer function.
The Nyquist criterion, a graphical
technique for determining the stability
of a system, and the root-locus
procedure, which allows adjustment
of the system poles by changing the
feedback system’s static gain, allow
you to use the open-loop transfer
function to predict closed-loop system
performance.Once you have a stable, closed-loop system, the main reasons for using feedback control are command following, disturbance rejection, insensitivity to modeling errors, and insensitivity to unmodeled high-frequency dynamics and noise. Time delays can be deadly, however. Always conserve phase, the equivalent of time delay. Integral control adds 90° of phase lag at every frequency, and digital control adds time delay primarily due to digital-to-analog conversion. Imagine trying to make decisions using old information.
High control gain yields good command tracking and good disturbance rejection. However, areas of concern include roll-off, saturation, and noise. Even the most insignificant detail of control engineering may prove important. Real control systems must be reliable, especially if people’s lives depend on them.
Maybe you know all of this information, but it is worth repeating. Let’s put some of this theory into practice. A case study at www.designnews.com bridges the theory-practice gap regarding something you all must be able to do: implement speed control of a motor with an attached incremental optical-encoder sensor using a microcontroller with a PWM output to drive an H bridge. This exercise uncovers gaps that many of us are aware of. The case study uses the popular, inexpensive Arduino microcontroller, a 12V Pitman brushed-dc motor, a three-channel optical encoder with 500 counts per revolution, the L298 H bridge, and MatLab/Simulink real-time code generation. I resolve to continue bridging the theory-practice gap with articles and Web-site case studies. Happy New Year.
Kevin C Craig, PhD,
is the Robert C Greenheck
chairman in engineering
design and a professor of
mechanical engineering at
the College of Engineering
at Marquette University.
For more mechatronic
news, visit mechatronicszone.com.Talkback
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Please post the link to the case study.
Rich LeGrand - 2012-5-2 06:32:34 PST -
I don't think that there is an article. I searched for the keywords: case study arduino matlab simulink pitman as well as several subsets on the EDN website and only came up with this article. Further, it hs been 5 days since requested and there has been no change or response. It's a shame. This article would have kick-started the school project with a strong kick.
Eager Reader - 2012-24-1 12:10:41 PST -
I second the request to fix the links. The "exercise" would be very instructive to my daughter in engineering school *right now*, and a cursory search of the website did not find it.
Eager Reader - 2012-24-1 10:01:55 PST -
Feedback systems only look simple if you don't understand them. The more that you understand them the more complex they look, and the more complex they get. On the other side, we do get lots of practice with feedback systems, from drinking our coffee to driving down the road. Time delay is the main cause of instability, but nonlinearity is what makes the systems less stable than where we adjusted them. That fact is always with us. That is because the gain or delay are different at other points. What makes the process difficult is that often feedback is used to compensate for the nonlinearity that we know about. Of course, knowing about the cause of a problem does not make the solution easy, only possible. And just because a solution is possible does not mean that it is practical. That is why feedback systems are such an interesting challenge, especially for engineers.
William Ketel - 2012-19-1 15:28:02 PST -
Please update the links to the case study and to mechatronicszone.com. The first is too general and the search engine does not find the case study, and the second goes nowhere.
L Stephens - 2012-19-1 11:07:40 PST
